Finding E_J Value of a Qubit: Step-by-Step Guide

[ramyasuresh]

Hi everyone,

I’ve performed microwave measurements on a 3D transmon and want to find the E_J value of the qubit. I’ve tried searching through many papers, particularly Koch et al, about how to do this, but I am stumped. Could someone please help me out?

Thanks in advance.

 

[A. Neumaier]

What is Koch et al.? Please give a link, also to an explanation of what a transmon is

 

[f95toli]

A transmon is a type of superconducting qubit.
Koch et al refers to a a series of papers from the Yale group.

What type of measurements have you done? Was it a fixed or variable frequency transmon?
Have you determined Ec? Could you get an idea of Ej by looking at the Ej/Ec ratio via the band structure?
I don't think there is a "direct" measurement of a Ej in a 3D transmon (most of the time we just "measure" it by measuring the resistance of a test junction fabricated at the same time) ; you would need to fit the theoretical expressions to different types of spectroscopy data .

 

[ramyasuresh]

A transmon is a type of superconducting qubit.
Koch et al refers to a a series of papers from the Yale group.

What type of measurements have you done? Was it a fixed or variable frequency transmon?
Have you determined Ec? Could you get an idea of Ej by looking at the Ej/Ec ratio via the band structure?
I don't think there is a "direct" measurement of a Ej in a 3D transmon (most of the time we just "measure" it by measuring the resistance of a test junction fabricated at the same time) ; you would need to fit the theoretical expressions to different types of spectroscopy data .

Thanks for your reply! I guess I should have made my question a bit more lucid; I had the data of a two-tone spectroscopic measurement (which yielded the avoided crossing plot of a variable frequency transmon with a 3D cavity). This was all I had at the moment, from which I had to find Ec, Ej, etc.

Which theoretical expressions would I have to fit to this? I found an approximated version in lecture notes from a 2011 Les Houches School. The transition frequency of the qubit is given by $\sqrt{8EcEj} - Ec$. However, it's explicitly mentioned that it's an approximation. Is there any reference from which I can obtain the original/exact expression (for understanding purposes).